Related papers: K3 Surfaces, N=4 Dyons, and the Mathieu Group M24

A CHL model is the quotient of $\mathrm{K3} \times E$ by an order $N$ automorphism which acts symplectically on the K3 surface and acts by shifting by an $N$-torsion point on the elliptic curve $E$. We conjecture that the primitive…

This thesis studies some examples of families of K3 surfaces with Picard lattices of maximal rank. These families occur as invariants of finite automorphism groups. The Picard-Fuchs differential equations describing the variation of Hodge…

We investigate F-theory models with a discrete $\mathbb{Z}_2$ gauge symmetry and $SU(n)$ gauge symmetries. We utilize a class of rational elliptic surfaces lacking a global section, known as Halphen surfaces of index 2, to yield genus-one…

It is known that the automorphism group of any projective K3 surface is finitely generated [24]. In this paper, we consider a certain kind of K3 surfaces with Picard number 3 whose automorphism groups are isomorphic to congruence subgroups…

The Matrix theory description of Type IIA string theory on a compact K3 surface as the theory of Neveu-Schwarz five-branes on $\tilde{K3}\times S^1$ is analyzed. The full multiplet of space-time BPS states is identified in the five-brane…

Motivated by an analogous result for K3 models, we classify all groups of symmetries of non-linear sigma models on a torus T^4 that preserve the N=(4,4) superconformal algebra. The resulting symmetry groups are isomorphic to certain…

We review the geometry of K3 surfaces and then describe this geometry from the point of view of an approximate metric of Gibbons-Hawking form. This metric arises from the M-theory lift of the tree-level supergravity description of type IIA…

In this paper we complete the classification of the elliptic fibrations on K3 surfaces which admit a non-symplectic involution acting trivially on the N\'eron--Severi group. We use the geometric method introduced by Oguiso and moreover we…

We introduce the notion of a combinatorial K3 surface. Those form a certain class of type III semistable K3 surfaces and are completely determined by combinatorial data called curve structures. Emphasis is put on degree $2$ combinatorial K3…

We study the symplectic topology of certain K3 surfaces (including the "mirror quartic" and "mirror double plane"), equipped with certain K\"ahler forms. In particular, we prove that the symplectic Torelli group may be infinitely generated,…

Let X be a complex algebraic K3 surface or a supersingular K3 surface in odd characteristic. We present an algorithm by which, under certain assumptions on X, we can calculate a finite set of generators of the image of the natural…

For a K3 surface over an algebraically closed field of odd characteristic, the representation of the automorphism group on the global two forms is finite. If the K3 surface is supersingular, it is isomorphic to the representation on the…

We study the twisted elliptic genera of 2d $(0,4)$ SCFTs associated with the BPS strings in the twisted circle compactification of 6d rank-one $(1,0)$ SCFTs. Such objects can arise when the 6d gauge algebra allows outer automorphism, thus…

We classify all the possible configurations of singular fibers and the torsion parts of Mordell-Weil groups of complex elliptic K3 surfaces. The complete list of 3279 configurations is attached.

We introduce a sequence of families of lattice polarized $K3$ surfaces. This sequence is closely related to complex reflection groups of exceptional type. Namely, we obtain modular forms coming from the inverse correspondences of the period…

We study the derived categories of twisted supersingular K3 surfaces. We prove a derived crystalline Torelli theorem for twisted supersingular K3 surfaces, characterizing Fourier-Mukai equivalences in terms of isomorphisms between their…

We study isogenies between K3 surfaces in positive characteristic. Our main result is a characterization of K3 surfaces isogenous to a given K3 surface $X$ in terms of certain integral sublattices of the second rational $\ell$-adic and…

To pave the way for the journey from geometry to conformal field theory (CFT), these notes present the background for some basic CFT constructions from Calabi-Yau geometry. Topics include the complex and Kaehler geometry of Calabi-Yau…

We present a detailed study of elliptic fibrations on Fourier-Mukai partners of K3 surfaces, which we call derived elliptic structures. We fully classify derived elliptic structures in terms of Hodge-theoretic data, similar to the Derived…

Motivated by the Swampland Distance and the Emergent String Conjecture of Quantum Gravity, we analyse the infinite distance degenerations in the complex structure moduli space of elliptic K3 surfaces. All complex degenerations of K3…